4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis
For mapping the original electronic structure Hamiltonian into the corresponding qubit Hamiltonian, we work in the second quantization formalism of quantum mechanics. Recall we introduced the first quantization in Section 4.1, Born-Oppenheimer approximation.
The Hartree-Fock (HF) method approximates an 
-body problem into 
one-body problems where each electron evolves in the mean field of the other electrons.
We can rewrite the electronic molecular Hamiltonian (
) as a linear combination of products of creation and annihilation operators (summarized in Figure 4.4):
where 
removes an electron from spin-orbital 
, and 
creates an electron in spin-orbital 
. The operation 
is the excitation operator, which excites an electron from the occupied spin-orbital 
into the unoccupied orbital 
. Constructing these were introduced in Section 2.1, Postulate 1 – Wave functions. The nuclear-nuclear ...
